The present invention is a method for improving the calibration of a Fourier transform ion cyclotron resonance mass spectrometer wherein the frequency spectrum of a sample has been measured and the frequency (f) and intensity (I) of at least three species having known mass to charge (m/z) ratios and one specie having an unknown (m/z) ratio have been identified. More specifically, the method uses known (m/z) ratios, frequencies, and intensities of at least three species to calculate coefficients, A, B, and C, wherein the mass to charge ratio of at least one of the three species (m/z)i is equal to       A          f      i        +      B          f      i      2        +            C      ·              G        ⁡                  (                      I            i                    )                            f      i      Q      
wherein fi is the detected frequency of the specie, G(Ii) is a predetermined function of the intensity of the specie, and Q is a predetermined exponent. Using the calculated values A, B, and C, the mass to charge ratio of the unknown specie (m/z)ii is calculated as the sum of       A          f      ii        +      B          f      ii      2        +            C      ·              G        ⁡                  (                      I            ii                    )                            f      ii      Q      
wherein fii is the measured frequency of the unknown specie, and (Iii) is the measured intensity of the unknown specie.
For human understanding of physical, biological, and chemical systems to progress, a need for ever greater accuracy in measuring species becomes a limiting factor for accurate insight into the operation of these systems. For example, with the increased availability of genomic databases, protein identification is now substantially based on searching an appropriate database with physico-chemical data obtained for that protein. Very often, mass spectrometric data from tandem mass spectrometry (MS/MS) experiments using peptides from protein digests are employed. One of the aspects of mass spectrometry, which is often viewed as the key to successful protein identification, is mass measurement accuracy (MMA). Increased mass accuracy allows the number of potential masses in a database to be reduced, and sufficiently high MMA may make a peptide unique within the context of a specific proteome.
Fourier transform ion cyclotron resonance (FTICR) mass spectrometry currently provides the best achievable mass accuracy. However, the mass accuracy in an FTICR experiment typically depends on the number of ions used for the measurement. When online separations are used, the analyte ion production rates vary widely, and the ion population in the trap cannot be easily or precisely controlled. Although mass accuracy in the sub-ppm level has been reported with internal calibration, external calibration methods currently known in the art typically don""t provide accuracies better than several ppm, particularly when the ion population for the measurement differs significantly from the ion population used for the calibration. In FTICR, the highest MMA have been obtained with small ion populations, often with the use of summation (or signal averaging) of many spectra, and of internal calibrants. However, if one desires a large dynamic range, large trapped ion populations are desired, which irrevocably causes relatively large space charge induced frequency shifts, and poorer MMA.
The widely varying ion populations that result from online separation constitute the greatest challenge. The difficulties for large ion populations in FTICR arise due to Coulomb mediated interactions between the different ions present in the cell (and their interactions with their image charge on the detection electrodes), which cause variations in measured frequencies. It has recently been demonstrated in Bruce, J. E.; Anderson, G. A.; Brands, M. D.; Pasa-Tolic, L.; and Smith, R. D. J. Am Soc Mass Spectrom 2000, 11, 416-421 the entire contents of which are incorporated herein by this reference, that the frequency shifts induced by coulombic interactions can be compensated for by correcting the detected frequencies, so as to align the deconvoluted spectrum of multiple charge states of the same peptide or protein. This approach provides most of the advantages associated with internal calibrant without its disadvantages. This procedure has allowed a significant improvement in mass accuracy for peptides in LC/FTMS experiments, but the mass accuracy realized still plateaus at the few ppm level due to the large variations in space charge effects.
All calibration procedures for ICR have, up to now, incorporated the space charge effect as a global effect resulting only from the number of charges in the trap. However, some frequency perturbations are known to depend on the frequency spacing between ions, e.g. the xe2x80x9cpeak-coalescencexe2x80x9d phenomenon. It is clear that the contribution of such smaller effects is obscured by the global space charge effect, and until now, little experimental evidence of xe2x80x9clocalxe2x80x9d frequency perturbations has been reported by Huang, J. Y.; P. W. Tiedemann, Land, D. P.; McIver, R. T; Hemminger, J. C. Int. J. Mass Spectrom. Ion Proc. 1994, 134(1), 11-21, the en ire contents of which are incorporated herein by this reference. Indeed, some authors have suggested that such an effect doesn""t exist Easterling, M. L.; Mize, T. H.; Amster, I. J., Anal. Chem. 1999, 71, 624-632.
In FTICR, the measured quantity is the effective (cyclotron) frequency of the ions, f. This frequency is then converted to an m/z value using a calibration function. The most widespread used calibration function is (1):                               m          z                =                              A            f                    +                      B                          f              2                                                          (        1        )            
This calibration law (1) was originally derived by Gross and coworkers as reported in Ledford, E. B.; Rempel, D. L.; Gross, M. L. Anal. Chem. 1984, 56, 2744-2748, the entire contents of which are incorporated herein by this reference, using results as reported in Jeffries, J. B.; Barlow, S. E.; Dunn, G. H. Int. J. Mass Spectrom. Ion Processes 1983, 54, 169-187 and Francl, T. J.; Sherman, M. G.; Hunter, R. L.; Locke, M. J.; Bowers, W. D.; McIver, R. T. Int. J. Mass Spectrom, Ion Processes 1983, 54, 189-199 the entire contents of which are also incorporated herein by this reference. According to these references, the derivation of the second term, B/f2, accounts for both the DC trapping field and the space charge influence. The space charge is assumed to be generated by all ion species present in the ICR cell during collection of the time domain signal. The two calibration coefficients A and B thus are theorized to account for factors important for the FTICR mass measurement, i.e. magnetic field strength, and radial components of the trapping DC electrostatic field and the space charge field. Although an additional third-order frequency term can be added to the calibration function (1), there are no quantitative reports on its importance for the improvement of calibration quality
This calibration technique assumes that the space charge is generated by all ion species present in the ICR cell during collection of the time domain signal. While this xe2x80x9cglobalxe2x80x9d space charge correction has been shown to improve accuracy of the mass calibration under conditions typical for bio-molecular studies, when the ion population in the ICR cell may vary in a broad range, it still suffers from drawbacks that hinder its accuracy. For example, the concept of a xe2x80x9cglobalxe2x80x9d space charge correction assumes that only the total trapped ion charge is significant for the mass calibration and fails to account for the possibility that the coherent motion of ions having the same m/z is influenced by other m/z ions differently than by the ions themselves. Such a situation may occur, for example, when the ion cloud motion can be, to a good approximation, described in terms of its center-of-mass motion. In this case the coulombic interactions of the same m/z ions, constituting the ion cloud, will be balanced and will not produce a net effect on the center-of-mass motion of the ion cloud. Under these conditions, accurate mass measurements must account for the coulombic interactions of the same m/z ions, constituting the ion cloud, since they will be balanced and will not produce a net effect on the center-of-mass motion of the ion cloud. Thus, there remains a need for improved methods for calibrating Fourier transform ion cyclotron resonance mass spectrometers.
Accordingly, it is an object of the present invention to provide an improved method for calibrating a Fourier transform ion cyclotron resonance mass spectrometer (FTICRMS).
It is another object of the present invention to provide an improved method for calibrating a FTICRMS that accounts for the coherent motion of ions having the same m/z as being influenced by other ions having different m/z.
It is another object of the present invention to provide an improved method for calibrating a FTICRMS that accounts for the motion of ions having the same m/z as being influenced by other ions having different m/z.
These and other objects of the present invention are accomplished by the following method for improving the calibration of a FTICRMS. As is customary in the operation of FTICRMS instruments, the frequency spectrum of a sample is first measured within the FTICRMS. The frequency (f) and intensity (I) of at least three species having known mass to charge (m/z) ratios, and one specie having an unknown (m/z) ratio, are then identified. Using the known (m/z) ratios, frequencies, and intensities of the three known species, three coefficients, A, B, and C, are then calculated, wherein the mass to charge ratio of at least one of the three species (m/z)i is equal to       A          f      i        +      B          f      i      2        +            C      ·              G        ⁡                  (                      I            i                    )                            f      i      Q      
and wherein fi is the detected frequency of the known specie, G(Ii) is a predetermined function of the intensity of the known specie, and Q is a predetermined exponent. A, B, and C may be calculated using any commonly known method; preferably a least squares fit or by solving three simultaneous equations. As will be readily apparent to those having skill in the art, when practicing the invention using more than three known species a corresponding number of coefficients can also be calculated, and the number of simultaneous equations solved to arrive at accurate values for those coefficients is adjusted. For example, when practicing the invention using four known species, a fourth coefficient, D, is also calculated and a fourth term using coefficient D,       D    ·          G      ⁡              (                  I          i                )                  f    i    Q  
is also calculated. More generally, the present invention should be understood to include up to an infinite series of terms calculated using a corresponding number of known species, each having a unique coefficient represented by the variable S,             S      ·              G        ⁡                  (                      I            i                    )                            f      i      Q        .
Accordingly, the scope of the present invention is intended to cover all such methods whereby three or more known species are utilized and three or more coefficients are calculated and the description herein describing the method as practiced with three coefficients should in no way be seen as limiting the scope of the invention.
Using the calculated values for A, B, and C, the mass to charge ratio of the unknown specie (m/z)ii is then calculated as the sum of       A          f      ii        +      B          f      ii      2        +            C      ·              G        ⁡                  (                      I            ii                    )                            f      ii      Q      
wherein fii is the measured frequency of the unknown specie, and (Iii) is the measured intensity of the unknown specie. As will also be apparent to those having skill in the art, the entire process is preferably automated using a computer equipped with a general purpose microprocessor and software written to perform the desired calculations. More preferred is the use of the microprocessor and software that are designed as integral to, or at least interface with, microprocessor and software which are utilized to control the FTICRMS and which measure the frequency and intensity of species within the FTICRMS. In this manner, the entire process can be automated and formed as an integral function of the operation of the instrument. Those having skill in the art will recognize that a great variety of possible configurations for this computer equipment and software are possible, and while the particular algorithm selected to implement the present invention is a merely a design choice that will depend primarily on the particular instrument being modified or constructed to practice the present invention, any such modification that performs the method described herein should be considered as falling within the scope of the invention. In the most general sense, the function G(Ii) may be any function that provides an accurate result. Exemplary functions include, but are not limited to G(Ii)=IiP, wherein P is greater than 0 and less than or equal to 10 and G(Ii)=lnII. As will be apparent to those having skill in the art, when the present invention is practiced using more than three coefficients, the additional terms corresponding to the additional coefficients also have predetermined functions. These predetermined functions may be the same across the terms, or they may vary. The selection of which functions to use in each term calculated according to the present invention to achieve the best accuracy will be dependant on the specific instrument and its operating conditions, and the error introduced by that instrument and its operating conditions.
Similarly, in the most general sense, the exponent Q is an exponent selected to correspond to the selected function G(Ii) to provide an accurate result. Preferably, exponent Q is selected as between 0 and 10. In a first preferred embodiment of the present invention, where three coefficients are calculated, G(Ui) is selected as equal to Ii and Q is selected as 2. In a second preferred embodiment, G(Ii) is selected as equal to in Ii and Q is selected as 3. The particular function and exponent selected may depend on a variety of factors, for example, they may depend on systemic errors that are specific to the configuration of a particular instrument. However, all such variations will have in common the use of the term which relates the coefficient C, the intensity of the frequency of the known and unknown species, and the measured intensity of the known and unknown species, to form a more accurate calibration of the instrument, and any such variations should be considered as falling within the scope of the present invention. As will be apparent to those having skill in the art, when the present invention is practiced using more than three coefficients, the additional terms corresponding to the additional coefficients also have predetermined exponents, Q. These predetermined exponents may be the same across the terms, or they may vary. In circumstances where the exponents are varied, they may vary in a geometric or linear progression. For example, if the exponent that corresponds to coefficient C is Q, in certain applications, the exponent that corresponds to coefficient D could be selected as Q+1, with the exponent that corresponds to coefficient E selected as Q+2, and so forth. The selection of which exponents to use in each term calculated according to the present invention to achieve the best accuracy will again be dependant on the specific instrument and its operating conditions, and the error introduced by that instrument and its operating conditions.
A further refinement of the present invention may be found by the addition of a term that makes the calibration procedure insensitive to the units of ion intensity. An example of this embodiment of the present invention may be illustrated by considering a calibration function having 4 terms. As previously described, in practicing this embodiment of the present invention, four calibrants, or ion species having known m/z, intensity and frequency values, are used to calculate calibration coefficients A, B, C and D. These may be calculated directly from simultaneous equations, or if more than four calibrants are available, A, B, C and D may also be calculated by means of the least square fit procedure. Either procedure results in a solution for the calibration coefficients, as set forth in the exemplary calibration function below.             (              m        /        z            )        i    =            A              f        i              +          B              f        i        2              +                            C          ·          ln                ⁢                  xe2x80x83                ⁢                  (                      I            i                    )                            f        i        3              +          D              f        i        3            
The calibration procedure may then be made insensitive to the units of ion intensity by manipulation of the 4-th term D/f3.
Multiplication of the ion intensity Ii by an arbitrary scale factor S results in additional term:                     C        ·        ln            ⁢              xe2x80x83            ⁢              (                  S          ·                      I            i                          )                    f      i      3        =                              C          ·          ln                ⁢                  xe2x80x83                ⁢                  (                      I            i                    )                            f        i        3              +                            C          ·          ln                ⁢                  xe2x80x83                ⁢                  (          S          )                            f        i        3            
Thus, scaling Ii by S is equivalent to adding Cxc2x7ln(S) to the D calibration coefficient. It follows that the calibration function is automatically adjusted for any units of ion intensity.
The subject matter of the present invention is particularly pointed out and distinctly claimed in the concluding portion of this specification. However, both the organization and method of operation, together with further advantages and objects thereof, may best be understood by reference to the following description taken in connection with accompanying drawings wherein like reference characters refer to like elements.